Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C271⋊C8 | C2 | semidirect |
| 3. #31773976 | C2 | semidirect |
| 4. #31773974 | C2 | semidirect |
| 5. #31773953 | C2 | semidirect |
| 6. C4×#16864637 | C2 | semidirect |
| 7. C8×Q8×C271 | C2 | semidirect |
| 53. C271⋊C8 | #41 | semidirect |
| 54. Q8×C271 | M16 | semidirect |
| 59. C8×C271 | #41 | semidirect |
| 75. C271 | #2971 | semidirect |
| 79. C8×Q8 | D271 | semidirect |
| 120. Q8 | #16864637 | semidirect |
| 135. C8 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864655 | 2 |
| Q8×C271⋊C8 | 2 |
| #31773976 | 2 |
| #31773974 | 2 |
| #31773953 | 2 |
| C4×#16864637 | 2 |
| C8×Q8×C271 | 2 |
| #2971 | 271 |